Slope-Intercept Form
Equation of a straight line.
Formula
Variables
Example
y = 2x + 1 has slope 2 and crosses the y-axis at (0, 1).
How it works
The slope-intercept form y = mx + b writes a straight line in a way that shows two key features immediately: the slope m and the y-intercept b. The slope tells how much y changes for each 1-unit increase in x, and the intercept gives the point where the line crosses the y-axis, which happens when x = 0. This works because every point on a non-vertical line can be described by starting at the intercept and then moving up or down at a constant rate.
When to use it
Use this form when you want to graph a line quickly or read its slope and y-intercept directly from the equation. It is also useful in word problems involving constant rates, like cost per item, distance over time, or simple linear growth.
Worked example, step by step
Suppose a line has equation y = -3x + 5. Step 1: Identify the slope and y-intercept. - m = -3 - b = 5 Step 2: Use the y-intercept to find one point on the line. - When x = 0, y = 5 - So one point is (0, 5) Step 3: Use the slope to find another point. - Slope = -3 = -3/1 - From (0, 5), move right 1 and down 3 - This gives the point (1, 2) Step 4: Check with the formula. - y = -3(1) + 5 - y = -3 + 5 - y = 2 So the line crosses the y-axis at (0, 5) and falls 3 units for every 1 unit you move right.
Common mistakes to avoid
- Mixing up the slope and the y-intercept
- Forgetting that the y-intercept is the value of y when x = 0
- Reading a negative slope as a positive rise instead of a downward change
Did You Know?
y = mx + b is probably the most-used equation in all of applied math — the workhorse of linear trends.
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